Graphical evaluation of Vmax and Km

The challenge faced by an experimenter is the determination of the two key parameters of the Michaelis-Menten equation, Vmax and Km, given a set of data pairs ([A]0i, v0ii i = 1,...,NA where N is usually 5 - 10. Actually, a deeper challenge awaits the experimenter, and that is to determine whether the fitting equation is a realistic description of the data. Nevertheless, suppose that we have established, from inspecting the Michaelis-Menten plot, that the data conform, at least roughly, to a rectangular hyperbola. Then we can make progress with the analysis by rearranging Eqn [2.1] into one of several possible forms that yield straight lines, when the newly transformed datavariables are plotted versus each other. The practical advantages of this mathematical manipulation are that (1) Vmax and Km can be determined readily by fitting a straight line to the transformed data; (2) departure of the data from a straight line are more readily detected by eye, than non-conformity to a rectangular hyperbola (these departures may indicate an inappropriateness of the simple model of the enzyme kinetics); and (3) the effects of inhibitors on the reaction can be more easily visualized.

It is worth noting that these data-transformation procedures, while being useful for providing initial estimates of parameters and for 'eye-balling' the data, do bias the error structure of the data and as such yield biased estimates of the kinetic parameters. Thus they have been superseded by non-linear regression for the final or definitive estimates of the parameters and their associated errors (see Chapter 6).

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